Constructive Analysis of Semicircular Elements: From Orthogonal Projections to Semicircular Elements

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Chapter 1 ■ Introduction
	1.1 Free Probability
	1.2 Semicircular Elements
	1.3 Some Free Random Variables Induced by Semicircular Elements
		1.3.1 Circular Elements
		1.3.2 Free Poisson Elements
	1.4 Joint Free Moments of Multi Semicircular Elements
	References
Chapter 2 ■ Semicircular Elements Induced by p-Adic Number Fields Q[sub(p)]
	2.1 Analysis of the p-Adic Number Fields Q[sub(P)]
	2.2 Statistical Models Induced by Q[sub(P)]
	2.3 Representations of (M[sub(p)], φ[sub(P)])
	2.4 Measure-Theoretic Models On {M[sub(p)]}[sub(p∊P)]
	2.5 C*-Subalgebras S[sub(p)] of (M[sub(p)], φ[sub(P,j)])
	2.6 Statistical Models for Banach *-Algebras LS[sub(p)] (j)
	2.7 On the Free Adelic Filterization LS
		2.7.1 Weighted-Semicircular Elements
		2.7.2 Weighted-Semicircular Elements of LS
		2.7.3 The Adelic Semicircular Filterization LS
	2.8 Circular Elements of LS
	2.9 Free Poisson Elements of LS Induced by U ∪ U
	2.10 Banach-Space Operators Acting On LS
	2.11 Pi-Shift Operators On LS
	References
Chapter 3 ■ Semicircular Elements Induced by Orthogonal Projections
	3.1 Some Banach *-Algebras Induced by Projections
	3.2 Weighted-Semicircular Elements Induced by Q
	3.3 Free-Distributional Data On L[sub(Q)]
	3.4 Circular Elements of L[sub(Q)]
	3.5 Free Poisson Elements of L[sub(Q)] Induced by U ∪ U
	3.6 Certain *-Isomorphisms Acting on L[sub(Q)]
	3.7 Group-Dynamical System On L[sub(Q)]
		3.7.1 Discrete-Group Dynamical Systems
		3.7.2 The Group-Dynamical System (B, L[sub(Q)], α)
		3.7.3 The Dynamical Semicircular *-Probability Space L[sub(Q)]
	3.8 Banach *-Probability Spaces L[sub(Q)][N]
	References
Chapter 4 ■ Certain Banach-Space Operators on L[sub(Q)] [N]
	4.1 The Integer-Shift-Operator Algebra B On L[sub(Q)]
	4.2 Restricted-Shift-Operator Algebras B[sub(N)] On L[sub(Q)][N]
	4.3 Free Probability On L[sub(Q)][N] Deformed by B[sub(N)]
	4.4 Conditional-Nilpotent-Property On B[sub(N)]
	4.5 Deformed Circular Laws On L[sub(Q)][N] by B[sub(N)]
	4.6 Deformed Free Poisson Distributions On L[sub(Q)][N] by B[sub(N)]
	4.7 The Semicircular ∞-Filterization L[sub(Q)][∞]
	4.8 More About L[sub(Q)][∞]
	References
Chapter 5 ■ Discussion
	References
Index